Existence and uniqueness of solutions for two- dimensional fractional non- colliding particle systems

  • Vu Thi Huong

    University of Transport and Communications, No 3 Cau Giay Street, Hanoi, Vietnam.
Email: vthuong@utc.edu.vn
Từ khóa: Stochastic differential equation, fractional Brownian motion, non- colliding particle systems.

Tóm tắt

In this paper, we consider the stochastic evolution of two particles with electrostatic repulsion and restoring force which is modeled by a system of stochastic differential equations driven by fractional Brownian motion where the diffusion coefficients are constant. This is the simplest case for some classes of non- colliding particle systems such as Dyson Brownian motions, Brownian particles systems with nearest neighbour repulsion. We will prove that the equation has a unique non- colliding solution in path- wise sense.

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